MANAGERIAL ECONOMICS & DECISION SCIENCES; OPERATIONS
Associate Professor of Managerial Economics & Decision Sciences
Queuing Systems
Service Management
We study a rental system where a fixed number of heterogeneous users rent one product at a time from a collection of re usable products. The online DVD rental firm Netflix provides the motivation. We assume that rental durations of each user are i.i.d. with finite mean. We study transient behavior in this system following the introduction of a new product that is desired by all the users. We represent the usage process for this new product in terms of an empirical distribution. This allows us to characterize the asymptotic behavior of the usage process as the number of users increases without bound, via appropriate versions of Glivenko-Cantelli and Donsker’s theorems. Analyzing the usage process, we demonstrate that an increase in the variability of the rental duration distribution can actually help the firm by allowing it to set lower capacity levels to provide a desired quality of service. Further, we show that the firm is better off not imposing any deadlines for the return of the product.
We consider the risk of a portfolio comprised of loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in the probability that the portfolio will incur large losses over a fixed time horizon. Contrary to the normal copula that is commonly used in practice (e.g., in the CreditMetrics system), we assume a portfolio dependence structure that supports {\it extremal dependence} among obligors and does not hinge solely on correlation. A particular instance within this model class is the so-called $t$-copula model that is derived from the multivariate Student $t$ distribution and hence generalizes the normal copula model. The size of the portfolio, the heterogenous mix of obligors, and the fact that default events are rare and mutually dependent makes it quite complicated to calculate portfolio credit risk either by means of exact analysis or naive Monte Carlo simulation. The main contributions of this paper are twofold. We first derive sharp asymptotics for portfolio credit risk that illustrate the implications of extremal dependence among obligors. Using this as a stepping stone, we develop multi-stage importance sampling algorithms that are shown to be asymptotically optimal and can be used to efficiently compute portfolio credit risk via Monte Carlo simulation.
We consider importance sampling simulation for estimating rare event probabilities in the presence of heavy-tailed distributions that have polynomial-like tails. In particular, we prove the following negative result: there does not exist an asymptotically optimal state-independent change-of-measure for estimating the probability that a random walk (respectively, queue length for a single server queue) exceeds a "high" threshold before going below zero (respectively, becoming empty). Furthermore, we derive explicit bounds on the best asymptotic variance reduction achieved by importance sampling relative to naive simulation. We illustrate through a simple numerical example that a good" state-dependent change-of-measure may be developed based on an approximation of the zero-variance measure
This paper analyzes a call center model with m customer classes and r agent pools. The model is one with doubly stochastic arrivals, which means that the m-vector λ of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of call center management are considered: staffing the r pools of agents, and dynamically routing calls to agents. The system manager’s objective is to minimize the sum of personnel costs and abandonment penalties. We consider a limiting parameter regime that is natural for call centers and relatively easy to analyze, but apparently novel in the literature of applied probability. For that parameter regime we prove an asymptotic lower bound on expected total cost, which uses a strikingly simple distillation of the original system data. We then propose a method for staffing and routing based on linear programming (LP), and show that it achieves the asymptotic lower bound on expected total cost; in that sense the proposed method is asymptotically optimal.
Motivated by applications in telephone call centers, we consider a service system model with m customer classes and r server pools. The model is one with doubly stochastic arrivals, which means that the m-vector λ of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of dynamic control are considered: customers may be either blocked or accepted at the time of their arrival, and then accepted customers of each class must be routed, either immediately upon acceptance or after some period of waiting, to a server pool that is qualified to handle that class. Customers who are made to wait before commencement of their service are liable to defect. The objective is to minimize the expected sum of blocking costs, waiting costs and defection costs over a fixed and finite planning horizon. We consider an asymptotic parameter regime in which (i) the arrival rates, service rates and defection rates are uniformly accelerated by a large factor κ, then (ii) arrival rates are increased by an additional factor g(κ), and the number of servers in each pool is increased by g(κ) as well. This produces a separation of time scales, justifying a pointwise stationary stochastic fluid approximation for our original system model. In the stochastic fluid approximation, optimal admission control and routing decisions are determined by a simple linear program that uses the current arrival rate vector λ as data. We explain how to implement the fluid model’s optimal control policy in our original service system context, and prove that the proposed implementation is asymptotically optimal in the first-order sense.
Motivated by applications in telephone call centers, we consider a service system model with m customer classes and r server pools. The model is one with doubly stochastic arrivals, which means that the m-vector ? of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of dynamic control are considered: customers may be either blocked or accepted at the time of their arrival, and then accepted customers of each class must be routed, either immediately upon acceptance or after some period of waiting, to a server pool that is qualified to handle that class. Customers who are made to wait before commencement of their service are liable to defect. The objective is to minimize the expected sum of blocking costs, waiting costs and defection costs over a fixed and finite planning horizon. We consider an asymptotic parameter regime in which (i) the arrival rates, service rates and defection rates are uniformly accelerated by a large factor ?, then (ii) arrival rates are increased by an additional factor g(?), and the number of servers in each pool is increased by g(?) as well. This produces a separation of time scales, justifying a pointwise stationary stochastic fluid approximation for our original system model. In the stochastic fluid approximation, optimal admission control and routing decisions are determined by a simple linear program that uses the current arrival rate vector ? as data. We explain how to implement the fluid model's optimal control policy in our original service system context, and prove that the proposed implementation is asymptotically optimal in the first-order sense.
We consider a call center model with multiple customer classes and multiple server pools. Calls arrive randomly over time, and the instantaneous arrival rates are allowed to vary both temporally and stochastically in an arbitrary manner. The objective is to minimize the sum of personnel costs and expected abandonment penalties by selecting an appropriate staffing level for each server pools. We propose a simple and computationally tractable method for solving this problem that only requires as input a few system parameters, and historical call arrival data for each customer class; in this sense the method is said to be data-driven. The efficacy of the proposed method is illustrated via numerical examples. An asymptotic analysis establishes that the prescribed staffing levels achieve near-optimal performance and characterizes the magnitude of the optimality gap.
Delay announcements informing customers about anticipated service delays are prevalent in service-oriented systems. How to use delay announcements to manage the service system in an efficient manner is a complex problem which depends on both the dynamics of the underlying queueing system and on the customer behavior.We examine this problem of information communication by considering a model in which both the firm and the customers act strategically: the firm in choosing its delay announcement while anticipating customer response, and the customers in interpreting these announcements and in making the decision about when to join the system and when to balk. We characterize the equilibrium language that emerges between the service provider and her customers. The analysis of the emerging equilibria provides new and interesting insights into customer-firm information sharing. We show that even though the information provided to customers is non-verifiable and non-credible, it improves the profits of the firm and the expected utility of the customers. Further, the information could be as simple as “High Congestion”/“Low Congestion” announcements, or could be as detailed as the true state of the system. We also show that firms may choose to shade some of the truth by using intentional vagueness to lure customers.
Many service providers use delay announcements to inform customers of anticipated delays. However, this information is usually not provided immediately, but rather after a short period of time (spent either waiting or occupied by the system). The focus of this paper is on the impact of this postponement on the ability of the firm to communicate non-verifiable congestion information to its customers as well as on the profits and utilities for the firm and the customers respectively. We show that this postponement can actually help the firm create credibility and augment the equilibrium language. However, in other settings this delay can also detract the equilibrium language. Further, we show that whenever credibility is created it improves not only the profit for the firm, but also the customers’ overall utility.
Recent times have witnessed the emergence of large-scale, web-based service marketplaces where many small service providers compete among themselves on catering to customers with diverse needs. Customers who frequent these marketplaces seek quick resolutions and thus usually trade-off prices with waiting times. The main goal of the paper is to discuss the role of the moderating firm in facilitating information gathering, operational efficiency, and communication among agents. Surprisingly, operational efficiency may be detrimental to the overall efficiency of the marketplace. Further, we show that to reap the "expected" gains of operational efficiency, the moderating firm may need to complement the operational efficiency by enabling communication among its agents. The study emphasizes the large-scale of such marketplaces and the impact it has on the outcomes.
Provision of real-time information by a firm to its customers has become prevalent in recent years in both the service and retail sectors. In this paper, we study a retail operations model where customers are strategic in both their actions and in the way they interpret information, while the retailer is strategic in the way it provides information. This paper focuses on the ability (or the lack thereof) to communicate credibly unverifiable nformation. We develop a game-theoretic framework to study this type of communication and discuss the equilibrium language emerging between the retailer and its customers. We show that for a single-retailer setting, the equilibrium language that emerges carries no information. In this sense, a single-retailer providing information on its own cannot create any credibility with the customers. We explore several remedies so that the firm can credibly disclose availability information to its customers. While in these remedies we show that the firm may be able to reveal complete information, the firm would prefer to shade some information and use intentional vagueness.
In this paper, we extend the concept of chaining introduced by Jordan and Graves (1995) for designing a robust supply chain network in which the link and nodes are susceptible to disruptions. We introduce the concept of fragility to quantify the change in system performance resulting from a disruption. Although one may anticipate that networks with longer chains will be more robust (smaller fragility) than shorter ones, our study reveals that this is not always true. We show that the fragility with respect to a single link failure decreases as the size of the chain decreases; however, the fragility with respect to a single node failure increases as the size of the chain increases. We also show that multiple failures in a network can be decomposed into a set of multiple subnetworks with a single failure; hence we can analyze the impact of large-scale disruptions by studying each single failure networks. Simulation experiments are used to extend insights from single link or node failures to multiple failure cases.
Generalizing earlier work on staffing and routing in telephone call centers, we consider a processing network with multiple server pools, jobs that may require several processing opera- tions, doubly stochastic input flows, differentiated processing modes, and other features as well. Given a finite planning horizon, we address the two-level problem of capacity choice and dynamic system control. A tractable modeling framework is proposed, in which a pointwise stationary fluid model (PSFM) is used to approximate the system’s dynamics. This framework allows one to develop practical policies with a computational burden that is manageable. Earlier work in more restrictive settings suggests that our method is asymptotically optimal in a parameter regime of practical interest, but this paper contains no formal limit theory. Rather, it develops a PSFM calculus that is broadly accessible, with an emphasis on modeling and practical computation.
We analyze the problem of product allocation to customers following the introduction of a new product in a closed rental system, such as Netflix. We consider two types of customers who differ in their rental time distributions. All customers desire the newly introduced product, and if a customer’s request for this product is denied, she receives a substitute product and requests for the new product upon return. We study the control problem of minimizing the mean delay encountered by customers before obtaining the new product in a large market setting. We show that asymptotically this problem is equivalent to solving a linear program that depends on the entire rental duration distribution as opposed to mean alone. The optimal policy turns out to be a mixed priority rule that prioritizes the slower customer class while maintaining a base allocation to the faster customer class to ensure quick return.
In recent times due to the commoditization of goods, many traditional firms often offer services as well. In this paper, we study the role of services apart from being another revenue source and understand how to manage services. We first understand their role in pricing of the underlying good. Next we study the impact of services on good variety offered by the firm. Lastly, we study the impact of services on markets of durable goods with its specific characteristics. We characterize the optimal behavior of the firm and relate that to concepts of bundling and market segmentation. We show that existence of services help firms offer a wider variety of underlying goods. Further, we show that in the market of durable goods, offering service resolve some of key problems such as time inconsistency.
This course counts toward the following majors:Operations.
Operations management is the management of business processes--that is, the management of the recurring activities of a firm. This course aims to familiarize students with the problems and issues confronting operations managers, and to provide the language, concepts, insights and tools to deal with these issues to gain competitive advantage through operations. We examine how different business strategies require different business processes and how different operational capabilities allow and support different strategies to gain competitive advantage. A process view of operations is used to analyze different key operational dimensions such as capacity management, cycle time management, supply chain and logistics management, and quality management. Finally, we connect to recent developments such as lean or world-class manufacturing, just-in-time operations, time-based competition and business re-engineering.
Prerequisite: DECS-433 or DECS-436.
Operations Management (Turbo) (OPNS-438-B)
This accelerated course serves as an introduction to Operations Management. The course approaches the discipline from the perspective of the general manager, rather than from that of the operations specialist. The coverage is very selective: Students concentrate on a small list of powerful themes that have emerged recently as the central building blocks of world-class operations. The course also presents a sample of operations management tools and techniques that have proved extremely useful through the years. The topics discussed are equally relevant in the manufacturing and service sectors.
Prerequisite: One-Year-student status.
This course counts toward the following majors: Operations.
In this course, we study demand-management decisions, and the methodology and systems required for making them. This course covers the mathematical models that underlie contemporary revenue management (RM) practices and also discusses recent advances in the area.
PHONE: 847-491-2529
FAX: 847-467-1220
Jacobs Center Room 565